But you do have to consider the transferable skills involved in what you learn.
If you study concept art you'll have skills that are great for working with concept art, but they're also pretty transferable to other forms of art.
Likewise, I study Ancient & Medieval history, so at the end of my degree, I should have the necessary skills to work in a job related to that field, whether it be research or heritage or teaching.
But those same skills are easily transferible to other areas of history, such as if I were to take up similar jobs related to say, colonial history, military history or modern history.
But, video game design is significantly more focussed on the tools required to create video games.
Would it give you the transferable skills to succeed in another IT related job? It might do, and I'm not at all knowledgable in those areas to say, but I personally would imagine it wouldn't.